ch-8

v2 m₂ m1 F21 F12 v1

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8.1

Two particles interac t

with each other. Accordin g to Newton’s third law, we must have

.

F

:

12 :F21

Momentum and Collisions

Chapter 8

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8.2

(Example 8.2) An archer fires an arrow horizontally. Because he is standing on frictionless ice, he will begin to slide across the ice.

Κ Beforedecay (at rest) p+ p– π– _π+ After decay π π 0

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8.3

(Example 8.3) A kaon at rest

decays into a pair of oppositely charged pions. The pions move apart with momenta of equal magnitudes but opposite directions.

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8.4

(a) A net force acting on a particle may vary in time. The impulse is the area under the curve of the magnitude of the net force versus time. (b) The average force (horizontal dashed line) gives the same impulse to the particle in the time interval t as the time-varying force described in part (a). The area of the rectangle is the same as the area under the curve.

t_i t_f ti F (a) tf t F (b) t F_avg Area = F_avg∆t

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8.5

A test dummy is brought to rest by an air bag in an automobile.

(Courtesy of Saab) Before After +2.60 m/s –15.0 m/s (a)

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8.6

(Example 8.4) (a) The car’s momentum changes as a result of its collision with the wall. (b) In a crash test, the

large force exerted by the wall on the car produces extensive damage to the car’s front end.

(T

im Wright/CORBIS)

p + + + He (b) m2 m1 (a) F₁₂ F₂₁ 4

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8.7

(a) A collision between

two objects as the result of direct contact. (b) A “collision” between two charged particles that do not make contact.

Before collision (a) m₁ m₂ v1i v2i After collision (b) vf m1 + m2 Figure 8.8

A perfectly inelastic head-on collision between two particles: (a) before the collision and (b) after the collision.

m1 m2 v_1i Before collision v_2i v_1f v_2f After collision (a) (b) Figure 8.9

An elastic head-on collision between two particles: (a) before the collision and (b) after the collision.

x k v_1f= (3.00iˆ) m/s v_2f m₁ m2 m1 m2 k v_1i= (4.00iˆ) m/s v_2i= (–2.50iˆ) m/s (a) (b)

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8.10

(Example 8.8) A moving block collides with another moving block with a spring attached: (a) before the

(a) Before the collision

v1i

(b) After the collision

θ φ _v 2f cos v1f cos v_1f sin v_1f v_2f –v2f sin φ φ θ θ m2 m1 Figure 8.11

θ (25.0iˆ) m/s y x v_f (20.0jˆ) m/s

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IGURE

8.12

(Example 8.10) An

eastbound car colliding with a northbound van.

CM (a) (b) (c) CM CM Figure 8.13

Two particles of unequal mass are connected by a light, rigid rod. (a) The system rotates clockwise when a force is applied between the less massive particle and the center of mass. (b) The system rotates counterclockwise when a force is applied between the more massive particle and the center of mass. (c) The system moves in the direction of the force without rotating when a force is applied at the center of mass.

y x z r_i ∆mi r_CM CM

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8.15

An extended object

can be modeled as a distribution of small elements of mass mi. The

center of mass of the object is located at the vector position , which has coordinates xCM, yCM, and zCM. r : CM A B A B C D Center of mass

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8.16

An experimental

technique for determining the center of mass of a wrench. The wrench is hung freely from two different pivots,

A and C. The intersection of the two

vertical lines AB and CD locates the center of mass.

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8.17

(Quick Quiz 8.5) A baseball bat cut at the location of its center of mass.

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8.18

(Example 8.11) Locating

the center of mass for a system of three particles. 4m x y 2m m O CM d b h

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8.19

(Example 8.12) (a) A triangular sign to be hung from a single wire. (b) Geometric construction for locating the center of mass. a x x O y c _b y dx dm (b) (a)

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8.20

Strobe photograph showing an overhead view of a wrench moving on a horizontal surface. The center of mass of the wrench (marked with a white dot) moves in a straight line as the wrench rotates about this point. The wrench moves from left to right in the photograph and is slowing down due to friction between the wrench and the supporting surface. (Note The decreasing distance between the white dots.)

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8.22

(Example 8.13) When a projectile explodes into several fragments, where does the center of mass of the fragments land?

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8.21

(Thinking Physics 8.1) A boy takes a

Figure Q8.13 Firefighters attack a burning house with a hose line.

Before (a) After (b) M v 2.00 m/s M 3M 3M Figure P8.5

60.0˚ x y 60.0˚ Figure P8.9 20 000 15 000 10 000 5 000 0 1 2 3 t (ms) F (N) F = 18 000 N Figure P8.7 Figure P8.11

A m1 m2 C B 5.00 m Figure P8.16 M m v v/2 Figure P8.18 5.00 m/s 3.00 m/s –4.00 m/s 10.0 kg 4.00 kg 3.00 kg Figure P8.22

y Figure P8.23 30 20 10 y (cm) x (cm) 10 20 30 Figure P8.33

53° 53° 0.100 nm 0.100 nm O H H Figure P8.34 Figure P8.35